A general approach to the problem of simultaneous computation of the discrete Fourier transform (DFT) of two sequences of length N , which may be real, imaginary, conjugated symmetric or conjugated anti-symmetric, using a single N -point DFT of a complex sequence is presented. The framework developed is applied to the simultaneous computation of two DFTs, one DFT and one inverse DFT (IDFT) or t...

In this paper, we propose one low-computation cycle and power-efficient recursive discrete Fourier transform (DFT)/inverse DFT (IDFT) architecture adopting a hybrid of input strength reduction, the Chebyshev polynomial, and register-splitting schemes. Comparing with the existing recursive DFT/IDFT architectures, the proposed recursive architecture achieves a reduction in computation-cycle by ha...

In a recent paper, Bourchard et al. [1] proposed the block sum transformation, a method intended as an alternative to the discrete Fourier transform (DFT), with application to the analysis of excited vibrations of linear systems. In this note, we mention the existence of a number of alternative algorithms for the computation of the DFT, and show that the block sum transformation is equivalent t...

The optical computing technology ooers new challenges to the algorithm designers since it can perform an n-point DFT computation in only unit time. Note that DFT is a non-trivial computation in the PRAM model. We develop two new models, DFT-VLSIO and DFT-Circuit, to capture this characteristic of optical computing. We also provide two paradigms for developing parallel algorithms in these models...

The Fast Fourier Transform (FFT) algorithm that calculates the Discrete Fourier Transform (DFT) is one of the major breakthrough in scientific computing and is now an indispensable tool in a vast number of fields. Unfortunately, software that provide fast computation of DFT via FFT differ vastly in functionality as well as uniformity. A widely accepted Applications Programmer Interface (API) fo...

A novel class of Discrete Fourier Transform algorithms is presented First, a new algorithm is presented for computing the DFT spectrum along any given direction. Then, computation of the entire DFT spectrum is computed using a minimal set of independent directions. It is shown that the new class of algorithms is both faster and more accurate than the traditional tensor decomposition of the DFT ...

The recent emergence of the discrete fractional Fourier transform (DFRFT) has caused a revived interest in the eigenanalysis of the discrete Fourier transform (DFT) matrix F with the objective of generating orthonormal Hermite-Gaussian-like eigenvectors. The Grünbaum tridiagonal matrix T – which commutes with matrix F – has only one repeated eigenvalue with multiplicity two and simple remaining...

Fractional Fourier transform (FRFT) is a generalization of Fourier transform, and it indicates a rotation of signal in the time-frequency plane[l). The FRFT has been widely successfully used in the many areas[l][2]. Because of the importance of FRFT, discrete fractional Fourier transform (DFRFT) becomes an important issue in recent years[3][4] [5][6]. In the development of DFRFT, the DFRFT has ...

In wireless communication, multiple receive-antennas are used with orthogonal frequency division multiplexing (OFDM) to improve the system capacity and performance. The discrete Fourier transform (DFT) plays an important part in such a system since the DFTs are required to be performed for the output of all those antennas separately. This paper presents area-time efficient systolic structures f...